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DTD Handbook

Handbook for Damage Tolerant Design

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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
      • 4. Residual Strength
        • 0. Residual Strength
        • 1. Introduction
        • 2. Failure Criteria
        • 3. Residual Strength Capability
        • 4. Single Load Path Structure
          • 0. Single Load Path Structure
          • 1. Abrupt Fracture
          • 2. Tearing Fracture
        • 5. Built-Up Structures
        • 6. References
      • 5. Analysis Of Damage Growth
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 4.4.1. Abrupt Fracture

4.4.1         Abrupt Fracture

For materials that exhibit abrupt failure, the start of slow crack extension will be followed immediately by the onset of rapid fracture.  The residual strength capability then requires a strict evaluation of the initial flaw sizes in the structure.  The allowable initial crack length necessary to maintain the required residual strength will be less than af ; the design limit load must also be such that the stress level in the structure is less than si , as shown in Figure 4.4.1.  The residual strength diagram can be evaluated as described earlier through the plot of sf vs. ac using the relationship K = sbÖpa for the structural geometry of interest and also employing the failure criterion based on a critical fracture toughness value, Kcr.  The margin of safety as shown in Figure 4.4.1 allows for undetected cracks or for subcritical crack growth such that the initial crack size will not become greater than af.


figure 4.1 picture

Figure 4.4.1.  Residual Strength Diagram Showing Defining Cracks and Residual Strength Parameters

The following example problem is presented to demonstrate the application of the steps in constructing the residual strength diagram and also to analyze the structure for its residual strength capabilities.  This example demonstrates the basic concepts involved in the residual strength capabilities of a single load path structure.


EXAMPLE 4.4.1         Residual Strength of Center Cracked Panel

Develop the residual strength diagram for the cracked finite width panel shown here.  The panel is 20 inches wide  and  0.375 inches thick with a length of 60 inches.  The yield strength (sy) for this material is 78 ksi and the fracture toughness (KIc ) is 40 ksi Öin.  The inspection procedure is a viual inspection capable finding a crack (2a) 2 inches long.


For the center-cracked geometry configuration shown, the stress-intensity factor K expresses by the relationship (see Section 11.3):


Since we have an explicit expression for K, using the fracture toughness failure criterion (plane strain), the residual strength diagram can be obtained directly.  The corresponding equation is



where KIc = 40 ksi Öin and W = 20 inch are given as data and sf  can be obtained for any selected crack length.  The sf  vs. ac curve, which is the required residual strength diagram, can now be plotted.

The residual strength sf  of the panel can be estimated from the equation that is described in the following diagram.  From this figure, for the given operating stress level (20 ksi), the critical crack size a at which unstable crack extension would occur can be estimated as 1.2 inches.  Thus, to avoid a fracture type failure of the panel, the structure should not develop a crack of this size.  Assume that based on an established visual inspection schedule, the simple rectangular aluminum panel, uniformly loaded in tension as shown, could develop a 2.0 inch long, central through-the-thickness crack (normal to loading) before detection.  This crack length is slightly smaller than the critical crack size (2a) of 2.4 (2 x 1.2 inch) under the operating conditions so that the margin of safety is small when this inspection process is employed.

plot for example 4.4.1

Residual Strength Diagram Determining Critical Crack Size at 20 ksi Operating Level


To establish the required residual strength level to fit the inspection schedule, the designer must reduce the crack-tip stress-intensity factor for the same applied load.  One method is to transfer portions of the load to a stiffening member.  Another method is to reduce the operating load level below the failure level corresponding to the inspection crack size, although this is not always practiced.